idealFromShelling -- Produces an ideal from a shelling

• Usage:

  I = idealFromShelling(P)

  I = idealFromShelling(S,P)

• Inputs:
  • S, a ring, (If omitted, it will use S=QQ[x_0..x_{n-1}] where n is the maximum integer in the lists of P.
  • P, a list, A list of lists of integers. Each list of integers is a facet of the complex and the order is a shelling.
  • S, a ring, (If omitted, it will use S=QQ[x_0..x_{n-1}] where n is the maximum integer in the lists of P.
• Outputs:
  • I, an ideal, generated by the monomials representing the minimal nonfaces of P

i1 : S = QQ[x_0,x_1,x_2,x_3,x_4]

o1 = S

o1 : PolynomialRing

i2 : P =  {{1, 2, 4}, {0, 1, 4}, {0, 2, 4}, {0, 3, 4}};

i3 : idealFromShelling(S,P)

o3 = monomialIdeal (x x x , x x , x x )
                     0 1 2   1 3   2 3

o3 : MonomialIdeal of S